Interval Estimates for the P-n Plots of Fatigue Data - with Special Reference to the Weibull Distribution

摘要

Probability papers for various fatigue life models such as normal, lognormal, exponential, gamma, Gumbel, Weibull distributions are graph papers with their coordinates modified so that, under the respective distributions, the probability failure, P in percent associated with the fatigue lifelength, N in number of cycles would form a straight line. Such graphical exhibits of fatigue data are known as P-N plots which are widely used by engineers to evaluate the fatigue characteristics of specimen, parts or structures. However, a P-N plot reveals only a series of point estimates for the true fatigue lifelength distribution function. In order to assess the 'goodness' of these point estimates, 'confidence intervals' are necessary. The report has concerned itself on three interval estimates. They are: (1) Nonparametric tolerance intervals, (2) Order statistic probability intervals, and (3) Parametric confidence intervals. These intervals are constructed around the P-N plots with a preassigned confidence coefficient. As the Weibull distribution is an important statistical model in fatigue testing, it is treated in some detail.